The temperaments listed are 58edo-distinct, meaning that they are all different even if tuned in 58edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

Period generator	Wedgie	Name	Complexity	Commas
58 19	<<14 1 -31]]		7.0510	6442450944/6103515625
29 10	<<30 -2 -73]]		15.837	9444732965739290427392/8381903171539306640625
58 1	<<16 -3 -42]]		8.828	4398046511104/4119873046875
29 9	<<2 -4 -11]]	Srutal	2.121	2048/2025
58 21	<<12 5 -20]]		5.522	254803968/244140625
29 1	<<26 6 -51]]		12.488	1641562064176545792/1490116119384765625
58 17	<<18 -7 -53]]		10.731	9007199254740992/8342742919921875
29 11	<<54 8 -113]]		26.555	[113 8 -54>
58 3	<<10 9 -9]]		4.502	10077696/9765625
29 8	<<34 48 -3]]		17.206	638131544614980078906888/582076609134674072265625
58 23	<<20 -11 -64]]		12.703	18446744073709551616/16894054412841796875
29 2	<<6 46 59]]		14.875	9007199254740992000000/8862938119652501095929
58 15	<<8 13 2]]	Unicorn	4.363	1594323/1562500
29 12	<<22 14 -29]]		9.851	2567836929097728/2384185791015625
58 5	<<22 43 17]]		13.625	328256967394537077627/312500
29 7	<<50 16 -91]]		23.481	[91 16 -50>
58 25	<<6 17 13]]	Gravity	5.177	129140163/128000000
29 3	<<38 40 -25]]		17.490	407943558924674501581996032/363797880709171295166015625
58 13	<<34 19 -49]]		15.323	654295038711035754184704/582076609134674072265625
29 13	<<10 38 37]]		11.672	1350851717672992089/1342177280000000000
58 7	<<4 21 24]]		6.600	10485760000/10460353203
29 6	<<18 22 -7]]		8.609	4016775629952/3814697265625
58 27	<<26 35 -5]]		12.886	1601009443167990624/1490116119384765625
29 4	<<46 24 -69]]		20.822	[69 24 -46>
58 11	<<2 25 35]]		8.326	858993459200/847288609443
29 14	<<42 32 -47]]		18.755	260789407250723664179754958848/227373675443232059478759765625
58 9	<<28 31 -16]]		13.029	40479843698864750592/37252902984619140625
29 5	<<14 30 15]]		9.338	205891132094649/200000000000000
2 1	<<0 29 46]]		10.202	70368744177664/68630377364883

7-limit temperaments

Period generator	Wedgie	Name	Complexity	Commas
58 19	<<14 1 33 -31 13 74]]		8.414	10976/10935 28672/28125
29 10	<<28 2 8 -62 -66 13]]		11.753	2401/2400 401408/390625
58 1	<<16 -3 17 -42 -18 48]]		7.540	1728/1715 28672/28125
29 9	<<2 -4 -16 -11 -31 -26]]		4.290	126/125 2048/2025
58 21	<<12 5 -9 -20 -48 -35]]		6.416	126/125 65536/64827
29 1	<<26 6 24 -51 -35 39]]		10.316	1728/1715 401408/390625
58 17	<<18 -7 1 -53 -49 22]]		8.928	2401/2400 28672/28125
29 11	<<4 -8 26 -22 30 83]]		7.609	2048/2025 19683/19600
58 3	<<10 9 7 -9 -17 -9]]		3.731	126/125 1728/1715
29 8	<<24 10 40 -40 -4 65]]		10.561	31104/30625 118098/117649
58 23	<<20 -11 -15 -64 -80 -4]]		11.806	28672/28125 50421/50000
29 2	<<6 -12 10 -33 -1 57]]		5.925	1728/1715 2048/2025
58 15	<<8 13 23 2 14 17]]		4.847	126/125 10976/10935
29 12	<<22 14 -2 -29 -65 -44]]		9.579	126/125 4194304/4117715
58 5	<<22 43 27 17 -19 -58]]		11.157	2401/2400 177147/175000
29 7	<<8 -16 -6 -44 -32 31]]		7.010	2048/2025 2401/2400
58 25	<<6 17 39 13 45 43]]		8.359	126/125 1605632/1594323
29 3	<<38 40 44 -25 -37 -10]]		14.346	126/125 97955205120/96889010407
58 13	<<24 39 11 6 -50 -84]]		11.703	1728/1715 1594323/1562500
29 13	<<10 -20 -22 -55 -63 5]]		9.999	2048/2025 50421/50000
58 7	<<4 21 -3 24 -16 -66]]		6.420	1728/1715 5120/5103
29 6	<<18 22 30 -7 -3 8]]		7.511	126/125 118098/117649
58 27	<<26 35 53 -5 11 25]]		12.079	126/125 645700815/645657712
29 4	<<12 34 20 26 -2 -49]]		8.457	2401/2400 19683/19600
58 11	<<2 25 13 35 15 -40]]		6.812	2401/2400 5120/5103
29 14	<<16 26 -12 4 -64 -101]]		10.753	31104/30625 65536/64827
58 9	<<28 31 37 -16 -20 -1]]		10.826	126/125 204073344/201768035
29 5	<<14 30 4 15 -33 -75]]		8.670	1728/1715 177147/175000
2 1	<<0 29 29 46 46 -14]]		9.402	5120/5103 50421/50000

11-limit temperaments

Period generator	Wedgie	Name	Complexity	Commas
58 19	<<14 1 33 35 -31 13 7 74 78 -16]]		7.910	176/175 243/242 5488/5445
29 10	<<28 2 8 12 -62 -66 -78 13 21 6]]		10.249	176/175 1344/1331 2401/2400
58 1	<<16 -3 17 11 -42 -18 -38 48 36 -28]]		6.539	176/175 540/539 1344/1331
29 9	<<2 -4 -16 -24 -11 -31 -45 -26 -42 -12]]		5.048	126/125 176/175 5488/5445
58 21	<<12 5 -9 1 -20 -48 -40 -35 -15 34]]		5.622	126/125 176/175 1344/1331
29 1	<<26 6 24 36 -51 -35 -33 39 63 18]]		9.209	176/175 540/539 33614/33275
58 17	<<18 -7 1 -13 -53 -49 -83 22 -6 -40]]		8.597	176/175 2401/2400 2560/2541
29 11	<<4 -8 26 10 -22 30 2 83 51 -62]]		6.610	176/175 243/242 896/891
58 3	<<10 9 7 25 -9 -17 5 -9 27 46]]		4.127	126/125 176/175 243/242
29 8	<<24 10 40 2 -40 -4 -80 65 -30 -133]]		10.411	540/539 3072/3025 3168/3125
58 23	<<20 -11 -15 21 -64 -80 -36 -4 87 111]]		10.79	441/440 3072/3025 3388/3375
29 2	<<6 -12 10 -14 -33 -1 -43 57 9 -74]]		5.898	176/175 540/539 896/891
58 15	<<8 13 23 -9 2 14 -42 17 -66 -105]]		6.251	126/125 540/539 896/891
29 12	<<22 14 -2 26 -29 -65 -35 -44 12 80]]		8.473	126/125 176/175 103680/102487
58 5	<<22 43 27 55 17 -19 11 -58 -21 61]]		10.247	243/242 441/440 43923/43750
29 7	<<8 -16 -6 20 -44 -32 4 31 102 77]]		7.436	243/242 441/440 2048/2025
58 25	<<6 17 39 15 13 45 3 43 -24 -93]]		7.341	126/125 243/242 896/891
29 3	<<20 18 14 -8 -18 -34 -82 -18 -81 -71]]		8.475	126/125 1728/1715 2560/2541
58 13	<<24 39 11 31 6 -50 -34 -84 -63 49]]		10.136	441/440 1728/1715 4000/3993
29 13	<<10 -20 -22 -4 -55 -63 -41 5 60 65]]		8.704	441/440 1344/1331 3388/3375
58 7	<<4 21 -3 -19 24 -16 -44 -66 -117 -43]]		7.574	441/440 896/891 1728/1715
29 6	<<18 22 30 16 -7 -3 -37 8 -39 -59]]		6.826	126/125 540/539 1344/1331
58 27	<<32 23 5 51 -38 -82 -30 -53 39 126]]		12.085	126/125 176/175 35831808/35153041
29 4	<<12 34 20 30 26 -2 6 -49 -48 15]]		7.373	243/242 441/440 4000/3993
58 11	<<2 25 13 5 35 15 1 -40 -75 -31]]		6.148	243/242 441/440 896/891
29 14	<<16 26 46 40 4 28 8 34 3 -47]]		8.504	126/125 243/242 5488/5445
58 9	<<28 31 37 41 -16 -20 -32 -1 -12 -13]]		9.390	126/125 540/539 12005/11979
29 5	<<14 30 4 6 15 -33 -39 -75 -90 3]]		7.939	441/440 1344/1331 1728/1715
2 1	<<0 29 29 29 46 46 46 -14 -33 -19]]		8.317	441/440 896/891 3388/3375

13-limit temperaments

Period generator	Wedgie	Name	Complexity	Commas
58 19	<<14 1 33 35 51 -31 13 7 29 74 78 115 -16 21 47]]		8.314	176/175 196/195 243/242 364/363
29 10	<<28 2 8 12 44 -62 -66 -78 -34 13 21 95 6 94 108]]		10.002	144/143 176/175 676/675 2401/2400
58 1	<<16 -3 17 11 21 -42 -18 -38 -26 48 36 60 -28 -4 32]]		5.970	144/143 176/175 196/195 364/363
29 9	<<2 -4 -16 -24 -30 -11 -31 -45 -55 -26 -42 -55 -12 -25 -15]]		5.517	126/125 176/175 196/195 364/363
58 21	<<12 5 -9 1 23 -20 -48 -40 -8 -35 -15 35 34 98 76]]		5.758	126/125 144/143 176/175 364/363
29 1	<<26 6 24 36 16 -51 -35 -33 -71 39 63 15 18 -44 -78]]		8.451	144/143 176/175 196/195 2200/2197
58 17	<<18 -7 1 -13 -9 -53 -49 -83 -81 22 -6 5 -40 -29 17]]		7.940	176/175 196/195 364/363 512/507
29 11	<<4 -8 26 10 -2 -22 30 2 -18 83 51 25 -62 -102 -44]]		6.128	144/143 176/175 351/350 676/675
58 3	<<10 9 7 25 -5 -9 -17 5 -45 -9 27 -45 46 -40 -110]]		4.810	126/125 144/143 176/175 196/195
29 8	<<24 10 40 2 46 -40 -4 -80 -16 65 -30 70 -133 -19 152]]		9.854	144/143 196/195 2205/2197 3267/3250
58 23	<<20 -11 -15 21 19 -64 -80 -36 -44 -4 87 85 111 109 -12]]		9.851	144/143 441/440 676/675 847/845
29 2	<<6 -12 10 -14 26 -33 -1 -43 19 57 9 105 -74 36 142]]		6.793	144/143 176/175 196/195 729/728
58 15	<<8 13 23 -9 25 2 14 -42 10 17 -66 10 -105 -15 120]]		5.948	126/125 144/143 196/195 676/675
29 12	<<22 14 -2 26 18 -29 -65 -35 -53 -44 12 -10 80 58 -34]]		7.584	126/125 144/143 176/175 847/845
58 5	<<22 43 27 55 47 17 -19 11 -7 -58 -21 -50 61 32 -41]]		9.188	243/242 351/350 441/440 1188/1183
29 7	<<8 -16 -6 20 -4 -44 -32 4 -36 31 102 50 77 11 -88]]		6.703	144/143 196/195 243/242 2200/2197
58 25	<<6 17 -19 15 -3 13 -47 3 -27 -92 -24 -70 108 62 -66]]		7.020	176/175 243/242 351/350 847/845
29 3	<<20 18 14 50 48 -18 -34 10 2 -18 54 45 92 83 -19]]		7.929	126/125 176/175 243/242 1188/1183
58 13	<<24 39 11 31 17 6 -50 -34 -62 -84 -63 -105 49 7 -56]]		9.414	144/143 351/350 441/440 847/845
29 13	<<10 -20 -22 -4 -34 -55 -63 -41 -91 5 60 -5 65 -14 -103]]		8.755	196/195 352/351 832/825 1001/1000
58 7	<<4 21 -3 39 27 24 -16 48 28 -66 18 -15 120 87 -51]]		7.182	176/175 351/350 676/675 847/845
29 6	<<18 22 30 16 20 -7 -3 -37 -35 8 -39 -35 -59 -55 10]]		6.197	126/125 144/143 196/195 364/363
58 27	<<26 35 53 7 45 -5 11 -79 -25 25 -105 -25 -164 -70 130]]		11.154	126/125 144/143 196/195 114345/114244
29 4	<<12 34 20 30 52 26 -2 6 38 -49 -48 -5 15 72 69]]		7.574	243/242 351/350 441/440 676/675
58 11	<<2 25 13 5 -1 35 15 1 -9 -40 -75 -95 -31 -51 -22]]		5.942	144/143 196/195 243/242 364/363
29 14	<<16 26 46 40 50 4 28 8 20 34 3 20 -47 -30 25]]		7.895	126/125 196/195 364/363 676/675
58 9	<<30 27 21 17 43 -27 -51 -77 -43 -27 -54 0 -25 43 86]]		9.223	126/125 144/143 364/363 1716/1715
29 5	<<14 30 4 6 22 15 -33 -39 -17 -75 -90 -60 3 47 54]]		7.123	144/143 351/350 364/363 441/440
2 1	<<0 29 29 29 29 46 46 46 46 -14 -33 -40 -19 -26 -7]]		7.496	196/195 352/351 364/363 676/675